Peter Smith's Blog, page 75

Interviews with philosophers at 3:AM

Probably most of people who happen across these blog posts will know of the series of interviews with philosophers conducted by Richard Marshall at 3:AM Magazine. These are often very readable and illuminating (and Marshall has an impressive ability to ask informed and pertinent questions right across the field).

What I have only just discovered is that there is a useful page giving links to the first 302(!) interviews here. So this post is just to spread the word to others who might be interested.

But I am struck how very opinionated the interviewees are. “Heavens, really …?” is my frequent reaction to the confident philosophical claims!  And indeed, I seem to find myself less and less sure of what I think about more or less any philosophical question as the years go on. (Which is, no doubt, why reverting to pure logic and other more mathematical things can be a blessed relief!).

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The Esmé Quartet, at the Wigmore Hall String Quartet Competition

The semi-finals and final of the Wigmore Hall String Competition were live streamed over the weekend.  Here is a recording of one of the semi-finals, well filmed with fine sound.

From 37.45, there is a performance of Beethoven’s Op. 59, No. 2 by the Esmé Quartet (four young South Koreans, based in the Berlin —  and the eventual winners). It seems to me that this is quite  astonishingly good. In the final, the Quartet play Schubert D887, bravely taking their time to wonderful effect. Having played together less than two years, they are indeed already hitting the heights.

As the Competition more widely shows, the future of quartet playing seems assured. Which is cheering. You can also watch the other semi-final and final here.

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Das Kontinuum 2018

Das Kontinuum was published a hundred years ago. It is very good to see that there is a conference in Leeds this autumn, 11–15 September to mark the occasion, focusing on recent research in predicativity. “It will bring together mathematicians, computer scientists and philosophers of mathematics working in areas related to the legacy of Hermann Weyl.” Promised speakers include Peter Aczel, Bahareh Afshari, Laura Crosilla, Michael Detlefsen, Gerhard Jäger, Graham E. Leigh, Øystein Linnebo, Maria E. Maietti, Per Martin-Löf, Takako Nemoto, Stephen Simpson and Nik Weaver.

The conference website is here.

Damn: I’m in Naples at the time — I would have been very interested to go. I do hope the organisers follow that increasingly common good practice of videoing presentations/posting papers on the website, for those of us who can’t make it.

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Onwards!

The twelfth birthday of this blog went by uncelebrated, but I guess it is a milestone of sorts.

While a number of good logic/maths blogs continue flourishing (see the sidebar!), many philosophy blogs do seem to be dropping by the wayside — becoming moribund or (like the long-running philosophy of religion Prosblogion) simply  disappearing. I wonder why philosophers are rather giving up on this relatively easy and relaxed way of talking to each other? Possibly, all the cool kids have moved on to something else (select Facebook groups, perhaps? — though I can’t say that that appeals, and even less so after recent shenanigans). Or very possibly, it’s a reflection of the fact that academic life is getting ever more stressed and time-pressured. I have the luxury of retirement, with no one looking over my shoulder.

Not that there haven’t been times over the last couple of years, with the world seeming to be going to hell in a handcart rather faster than usual, when it has been difficult to muster quite enough enthusiasm to write here about what are, after all, decidedly minor matters. But then, I enjoy being occasionally distracted  by other blogs; and enough people do seem to enjoy coming here to be distracted in their turn.

So onwards! Posts soon on exhibitions of Italian art, on philosophical logic books from back in the day which are worth another look, on the Pavel Haas Quartet (again), on some other quartets, on novels I’ve been (re)reading recently, and even some more logic matters. Well, a chap needs a hobby …

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Every perceptual experience is possibly delusory

(A) Take the following familiar kind of philosophical claim:

Every perceptual experience is possibly delusory!

How do you read this? Do you parse it as

(Every perceptual experience is such that)(it is possible that) it is delusory

or as

(It is possible that)(every perceptual experience is such that) it is delusory?

Do you think that one reading is correct (or at least the strongly preferred reading), and the other incorrect (or at least to be deprecated)? Or do you take (1) to be ambiguous between the ∀♢ reading (2) and the ♢∀ reading (3)?

Peter Geach in Reference and Generality takes it that (1) is unambiguously to be read as (3), with ‘every’ taking narrow scope. Or to be more accurate he talks — at p. 104 of the third edition —  about the fallacy in ‘the transition from “Any sense perception may be illusory” to “Every sense perception may be illusory”.’ I take it that the slight difference in wording is neither here nor there for the current point, and that the fallacy Geach is after is the fallacy of moving from ∀♢ to ♢∀. So indeed Geach is construing his  ‘every’ proposition as ♢∀ (and he doesn’t discern ambiguity).

Interestingly, however, when I asked [on Twitter] about (1), a couple of more-than-respectable voices in different necks of the logical woods agreed with Geach that (1) is not ambiguous — however, they claimed contra Geach that (1) is to be read as (2), i.e. ♢∀. Thus  “I don’t read [this] as ambiguous; [it] seems clearly to have the ∀♢ reading”. And “I can imagine situations where someone uses (1) to be ♢∀, but they’re all situations where someone is using [1] improperly or imprecisely”.

(B) Why is Geach so confident that in his ‘every’ proposition,  like in our (1), the quantifier has narrow scope, while in the corresponding ‘any’ proposition it has wide scope? For him, I think, this view goes with a more general view that ‘every’ takes narrow scope when ‘any’ takes wide scope. Thus contrast

If everyone loves Nerys, then Owen does,
If anyone loves Nerys, then Owen does.

Then, reasonably uncontroversially (and assuming no special emphasis on ‘anyone’), the normal readings of these propositions are different, and these will be regimented respectively as

with ‘every’ having narrow scope with respect to the conditional, and vice versa for ‘any’. Indeed, I can imagine Geach armed with his scope principle saying “I can imagine situations where someone uses (1) to be ∀♢, but they’re all situations where someone is using (1) improperly or imprecisely”!!

(C) I take the disagreement between Geach and my twitter correspondents to be a bit of evidence in favour of my own view that both sides are wrong, and that — in the no-doubt corrupted state of modern chat! — (1) is pretty much ambiguous as it stands between the readings (2) and (3).

Now, actually, I don’t want or need to hang anything on this claim in the bit of my intro logic book which I’m re-writing. For when it comes to such quantified claims, it will be agreed on all sides that you do have to take note of questions of scope, even if you disagree about the verdicts. And that’s the crucial point you want when explaining that quantifiers, unlike proper names, have scopes.

Still, I’d be interested to know what other people’s linguistic intuitions are here!  Are you in the No Real Ambiguity camp about (1), and if so do you jump with Geach to the ∀♢ reading, or with some others to the ♢∀ reading? Are you in the You Can Read It Either Way camp? Do you have some other example of an ordinary language proposition mixing a quantifier and a modality which is, you think, a more compelling example of ambiguity? Do tell!

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The stuff of nightmares

Once upon a time, John Corcoran and Stewart Shapiro reviewed a little book, by distinguished authors, from a distinguished press, What is Mathematical Logic edited by John N. Crossley for OUP. It’s the nightmare of getting to deserve a review like that which might rather slow a chap down as he tries to revise his own logic text …

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The Pavel Haas Quartet play Shostakovich’s 2nd Quartet

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Five books — Philosophy of Maths

You may very well know the Five Books website, where a wide-ranging cast of contributors are asked “to make book recommendations in their area of work and explain their choices in an interview”. The recommendations are often quirky, sometimes even slightly bizarre, but rarely without interest. It’s an illuminating and fun project.

There are a good number of topics in philosophy covered at Five Books, including some quite narrow ones. Though I am guessing that, reasonably enough, they are not going to get round to dealing with a topic of rather limited interest like the philosophy of mathematics. That thought sets me wondering: what five books in the area would I recommend in the same spirit as a Five Books posting. So here’s my selection — my selection today, at any rate: another day I might feel differently!

Modern philosophy of mathematics is still shaped by debates starting over a century ago, springing from the work of Frege and Russell, and also from Hilbert’s alternative response to the  “crisis in foundations”, and from the impact of Gödel’s work on the logicist and Hibertian programmes. All this is covered brilliantly and at relatively modest length in Marcus Giaquinto’s  The Search for Certainty: A Philosophical Account of Foundations of Mathematics (OUP, 2002) This is not just engaging and reliable but is written with very enviable clarity. (By all means, then go back to reading Frege’s Grundlagen, or dip into e.g. Bertrand Russell’s Introduction to Mathematical Philosophy. But you won’t find a better initial guide to those foundational debates than Giaquinto.)

Textbooks tend to present developed chunks of mathematics in a take-it-or-leave-it spirit, the current polished surface hiding away the earlier rough versions, the conceptual developments, the false starts. So Imre Lakatos’s Proofs and Refutations (originally 1963/4: CUP 1976) makes for a wonderful counterbalance. A classic exploration in dialogue form of the way that mathematical concepts are refined, and mathematical knowledge grows. We may wonder how far the morals that Lakatos draws can be generalised; but this remains a fascinating read.

The next book is a (too rare) example of a philosopher writing a mathematics book, engaging head-on with the conceptual issues the mathematics throws up. Michael Potter’s Set Theory and Its Philosophy (OUP 2004) is exactly what you need to read before trying to think about which brand of set theory (if any) to buy and why, or about the sense in which set theory is foundational, etc. The interplay between the mathematical and the philosophical here is very illuminating.

Many philosophers know a  bit about arithmetic and set theory: but there is a lot more to mathematics than that. If you want to engage philosophically with mathematics more widely, you need to have some sense of what is going on in some other areas of mathematics and to understand something of how these areas hang together (remember Sellars’s words about philosophy concerning itself with how things hang together …). I can’t think of a better place to start than with Saunders Mac Lane’s Mathematics: Form and Function (Springer 1986). You will need some, a little, mathematics to cope with this: but then you can’t hope to do the philosophy of X without knowing something about X! And this book is a remarkable achievement, written by a great mathematician with a genuine concern for some of the philosophical issues in the vicinity.

Thanks to the Stanford Encyclopedia and various series of Companions and Handbooks, it has never been easier to get up to speed with (fairly) recent work in various areas of philosophy. That’s certainly true in this area, thanks to Stewart Shapiro, ed., The Oxford Handbook of Philosophy of Mathematics and (Its) Logic (OUP 2005). Oddly the ‘its’ is missing from the book’s official title, but the essays here only talk about aspects of logic of concern to the philosophy of maths, and the ‘its’ is rightly there in the title of Shapiro’s own editor’s introduction. So here are 26 essays on aspects of the philosophy of mathematics and on relevant logical matters, written by a star cast, and — unlike many collections of this kind — at a pretty consistent level of accessibility and quality, and in some cases offering essays on opposing sides of major debates. Perhaps the overall coverage is slightly conservative in the choice of topics: but there is still a huge amount of interest here. If you don’t find a good proportion of these essays engaging and worthwhile, then mainstream philosophy of mathematics perhaps just isn’t for you.

So, with many regrets about what I’ve had to leave out, there are my suggestions for five books — I’d be very intrigued to hear yours!

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Formal Theories of Truth

No one can say that Jc Beall, Michael Glanzberg and David Ripley have rattled on at self-indulgent length in their new OUP book Formal Theories of Truth. Just 119 small pages of main text. My kind of book, these days!

It’s elegantly organized, lively and engaging. First a general but carefully spelt-out version of a Liar Paradox derivation is set out. Then various options for escape are outlined. There’s a chapter on changing our inference rules for connectives, a chapter on restricting the inferences between P and T[P], a chapter on digging into the substructure of our logic, a short chapter on other directions to take. This is one very neat way of putting some order into the ramifying debates of formal treatments of the Liar. (It reads like an extended Stanford Encylopedia article — and indeed, that’s in effect what it is.)

The book is aimed, the authors say, at interested readers ‘with a little bit of formal logic training (even a first course in logic) who wish to take a first step into so-called formal theories of truth’. I wonder if those who have taken just a first logic course will fully ‘get’ e.g. the snappy claim that a diagonal lemma can be proved in the right settings (pp. 31-32) or will understand talk about limit ordinals (p. 44), etc. I’m not usually one to ask for a longer book. But I think this one, in fact, gives a bumpier ride than some of the ‘budding philosophers’ in the target audience will be comfortable with, and could sometimes have gone more slowly. Will the reader who hasn’t already been given an arm-waving lecture explanation really pick up, e.g., the beautiful idea underlying Kripke’s theory?

Still, for readers who are perhaps a little past the budding stage, who have perhaps had some first fleeting encounters with a formal theory of truth or two, and are in need of a way of organizing and interrelating the fragments they know about, in order to get into a good position to move on to tackle more details, this can be warmly recommended as exactly the book they have been wanting.

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One that got away

We were looking the other evening for our copy of a lovely book, Nathan Silver’s 1968  Lost New York. I remember buying it second hand when we had no money, perhaps five years after it was first published, in the even-then old-fashioned warren that was Galloway and Morgan in Aberystwyth. The book is a  photographic essay on the lost buildings and streets of a past city. It is very evocative, not that I’ve ever been to New York, or now ever will (but then the city of the mind —  of Edith Wharton, say — is not there to be visited). But there’s something about glimpses of cities the day-before-yesterday, though I find it hard to put into words the deep appeal I find in them.

We couldn’t believe it that the book had gone. Somehow, in a mad moment, in one of those necessary fits of clearing out to keep at bay the ever over-flowing shelves, we must have looked at each other and said ‘have you looked at that in a dozen years or more? no?? then it should go to Oxfam!’. But we can’t remember how we ever came to agree that. For the book is a delight to browse in occasionally, and we were sentimentally attached to it. How odd.

So I have found a copy online, absurdly cheap. And here it is again. But not quite as we remember it — for this is a later reprint, and at least in our memory the original photographic reproductions were sharper, on glossier paper. But maybe our memories play us false, and it’s just that a replica isn’t quite the original with its own small history.

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